is a natural and useful identification of the real tangent space with the holomorphic part of the complex tangent space. See [1]},
in particular Section 2 of Chapter 0, for further discussions. With this identification \(\dot{z}\) 
represents the velocity of \(z(t)\) . Still one need to keep in mind that \(\dot{z}\)  is just a complex number and that it is rather
the preimage under \({\rm proj}\)  above that is the true velocity, as a real tangent vector.
